I.Tính giá trị biểu thức 8^10+4^10/8^4+4^11 II.Tìm X biết (X-1/2)^3=1/27 (X+1/2)^2=4/25 III.Tìm X thuộc Z biết 2^x-1=16 (X-1)^2=25

Đáp án :

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Giải thích các bước giải :

I .

$\frac{8^{10} + 4^{10}}{8^4 + 4^{11}} = $ $\frac{(2^3)^{10} + (2^2)^{10}}{(2^3)^{4} + (2^2)^{11} }$ $\\$ $=\frac{2^{30} + 2^{20}}{2^{12} + 2^{22}}$ $\\$ $=\frac{2^{20}(2^{10} + 1)}{2^{12}(1 + 2^{10})}$ $\\$ $= \frac{2^{20}}{2^{12}} = 2^8 = 256$

II. 

$\bigg(x – \frac{1}{2}\bigg)^{3}$ $=\frac{1}{27}$ $\\$ $=> \bigg(x – \frac{1}{2}\bigg)^{3}$ $=\bigg(\frac{1}{3}\bigg)^{3}$ $\\$ $=> x – \frac{1}{2} = \frac{1}{3}$ $\\$ $=> x = \frac{1}{3} + \frac{1}{2} = \frac{5}{6}$

$\bigg(x + \frac{1}{2}\bigg)^{2}$ $=\frac{4}{25} = \bigg($ $\frac{2}{5}\bigg)^2$

$=> x + \frac{1}{2} = \frac{2}{5} => x = $ $\frac{2}{5} – $ $\frac{1}{2} = $ $\frac{-1}{10}$

III.

$2^{x-1} = 16 => 2^{x – 1} = 2^4 => x – 1 = 4 => x = 5$

$(x – 1)^2 = 25 => (x – 1)^2 = \pm \big(5^2\big) => $$\left \{ {{x – 1=5} \atop {x – 1= – 5}} \right.=> $ $\left \{ {{x=6} \atop {x=-4}} \right.$